A series of hydroxyl-, methoxy-, and acetoxy-substituted 3- and 4-arylcoumarins were synthesized. All title compounds were screened for their antioxidant capacity, ability to scavenge the 1,1-diphenyl-1-picrylhydrazyl (DPPH) radical, and ability to chelate iron ions. Furthermore, all derivatives were assessed using molecular properties prediction and drug likeness using Molinspiration. It was found that all studied derivatives were potential candidates for further research, as they complied with Lipinski's rule of five for drug likeness. 3- or 4-arylcoumarins that possess two hydroxyl groups in ortho position, such as 4h, 5b, h, and 6a, had remarkable half-maximal effective concentration (EC50) for radical scavenging, with better performance than known antioxidants in DPPH and metal-chelating assays. In addition, the cupric-reducing antioxidant capacity and ferric-reducing antioxidant power of the synthesized compounds were investigated for antioxidant activity. Among them, 5g, h and 6a, b showed significantly better Trolox equivalent antioxidant capacity (TEAC) than standard compounds. The results demonstrate that the compounds with dihydroxyl groups at 6- and 7-positions of the benzopyrone ring of the arylcoumarin structure are the most active of the series as antioxidants. On the basis of these findings, these new coumarin derivatives are potential therapeutic candidates for pathogenesis of many diseases characterized by free-radical overproduction.